Login/Sign Up
If a, b, c are in A.P., then show that: $bc – {a^2},ca – {b^2},ab – {c^2}$
If a, b, c are in A.P., then show that: $bc – {a^2},ca – {b^2},ab – {c^2}$
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.5 | Maths | RD Sharma
If a, b, c are in A.P., then show that: $bc – {a^2},ca – {b^2},ab – {c^2}$

Answer:

If (ca – b2) – (bc – a2) = (ab – c2) – (ca – b2)

bc – a2, ca – b2, ab – c2 are in A.P.

Consider LHS and RHS,

(ca – b2) – (bc – a2) = (ab – c2) – (ca – b2)

(a – b2 – bc + a2) = (ab – c2 – ca + b2)

(a – b) (a + b + c) = (b – c) (a + b + c)

a – b = b – c

a, b, c are in AP,

b – c = a – b

Hence, the given terms are in AP

i

More Material